Series configured variable flow restrictors for use in a subterranean well

ABSTRACT

A well device can include a fluid diode having an interior surface that defines an interior chamber, and an outlet from the interior chamber, with the interior surface operable to direct fluid to rotate in a rotational direction through the outlet, and another fluid diode having an interior surface that defines an interior chamber in fluid communication with the outlet, the second interior surface operable to direct fluid to rotate in the rotational direction in response to receiving the fluid rotating in the rotational direction through the outlet. A method of controlling flow in a well can include communicating fluid through two or more fluid diodes in a flow path between an interior and an exterior of a well device in the well. Communicating the fluid through the fluid diodes can cause the fluid to rotate within the fluid diodes in a same rotational direction.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part of U.S. application Ser. No.12/879,846, filed 10 Sep. 2010, the entire disclosure of which isincorporated herein by this reference.

BACKGROUND

This disclosure relates generally to equipment utilized and operationsperformed in conjunction with a subterranean well and, in an exampledescribed below, more particularly provides a series configuration ofvariable flow restrictors.

In a hydrocarbon production well, it is many times beneficial to be ableto regulate flow of fluids from an earth formation into a wellbore. Avariety of purposes may be served by such regulation, includingprevention of water or gas coning, minimizing sand production,minimizing water and/or gas production, maximizing oil and/or gasproduction, balancing production among zones, etc.

In an injection well, it is typically desirable to evenly inject water,steam, gas, etc., into multiple zones, so that hydrocarbons aredisplaced evenly through an earth formation, without the injected fluidprematurely breaking through to a production wellbore. Thus, the abilityto regulate flow of fluids from a wellbore into an earth formation canalso be beneficial for injection wells.

Therefore, it will be appreciated that advancements in the art ofcontrolling fluid flow in a well would be desirable in the circumstancesmentioned above, and such advancements would also be beneficial in awide variety of other circumstances.

SUMMARY

In the disclosure below, a variable flow resistance system is providedwhich brings improvements to the art of regulating fluid flow in wells.One example is described below in which resistance to flow through avortex device is dependent on a rotation of a fluid composition as itenters the vortex device. Another example is described, in whichmultiple vortex devices are connected in series.

In one aspect, the disclosure provides to the art a variable flowresistance system for use in a subterranean well. The system can includea vortex device through which a fluid composition flows. A resistance toflow of the fluid composition through the vortex device is dependent ona rotation of the fluid composition at an inlet to the vortex device.

In another aspect, a variable flow resistance system described below caninclude a first vortex device having an outlet, and a second vortexdevice which receives a fluid composition from the outlet of the firstvortex device. A resistance to flow of the fluid composition through thesecond vortex device is dependent on a rotation of the fluid compositionat the outlet of the first vortex device.

In yet another aspect, a variable flow resistance system can include afirst vortex device which causes increased rotation of a fluidcomposition at an outlet of the first vortex device in response to anincrease in a velocity of the fluid composition, and a second vortexdevice which receives the fluid composition from the outlet of the firstvortex device. A resistance to flow of the fluid composition through thesecond vortex device is dependent on the rotation of the fluidcomposition at the outlet of the first vortex device.

A well device for installation in a wellbore in a subterranean zone isalso described below. In one example, the device includes a first fluiddiode comprising a first interior surface that defines a first interiorchamber, and an outlet from the first interior chamber, the firstinterior surface operable to direct fluid to rotate in a rotationaldirection through the outlet; and a second fluid diode comprising asecond interior surface that defines a second interior chamber in fluidcommunication with the outlet, the second interior surface operable todirect fluid to rotate in the rotational direction in response toreceiving the fluid rotating in the rotational direction through theoutlet.

The disclosure below also describes a method of controlling flow in awellbore in a subterranean zone. An example is described in which themethod comprises communicating fluid through a first fluid diode and asecond fluid diode in a flow path between an interior and an exterior ofa well device in the subterranean zone. Communicating the fluid throughthe first fluid diode and the second fluid diode can cause the fluid torotate within the first fluid diode in a rotational direction and torotate within the second fluid diode in the rotational direction.

These and other features, advantages and benefits will become apparentto one of ordinary skill in the art upon careful consideration of thedetailed description of representative examples below and theaccompanying drawings, in which similar elements are indicated in thevarious figures using the same reference numbers.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a representative partially cross-sectional view of a wellsystem which can embody principles of the present disclosure.

FIG. 2 is an enlarged scale representative cross-sectional view of awell screen and a variable flow resistance system which may be used inthe well system of FIG. 1.

FIGS. 3A & B are representative “unrolled” cross-sectional views of oneconfiguration of the variable flow resistance system, taken along line3-3 of FIG. 2.

FIG. 4 is a representative cross-sectional view of another configurationof the variable flow resistance system.

FIG. 5 is a representative cross-sectional of the variable flowresistance system of FIG. 4, taken along line 5-5.

FIGS. 6A & B are representative cross-sectional views the variable flowresistance system of FIG. 4, depicting changes in flow resistanceresulting from changes in characteristics of a fluid composition.

DETAILED DESCRIPTION

Representatively illustrated in FIG. 1 is a well system 10 which canembody principles of this disclosure. As depicted in FIG. 1, a wellbore12 has a generally vertical uncased section 14 extending downwardly fromcasing 16, as well as a generally horizontal uncased section 18extending through an earth formation 20.

A tubular string 22 (such as a production tubing string) is installed inthe wellbore 12. Interconnected in the tubular string 22 are multiplewell screens 24, variable flow resistance systems 25 and packers 26.

The packers 26 seal off an annulus 28 formed radially between thetubular string 22 and the wellbore section 18. In this manner, fluids 30may be produced from multiple intervals or zones of the formation 20 viaisolated portions of the annulus 28 between adjacent pairs of thepackers 26.

Positioned between each adjacent pair of the packers 26, a well screen24 and a variable flow resistance system 25 are interconnected in thetubular string 22. The well screen 24 filters the fluids 30 flowing intothe tubular string 22 from the annulus 28. The variable flow resistancesystem 25 variably restricts flow of the fluids 30 into the tubularstring 22, based on certain characteristics of the fluids.

At this point, it should be noted that the well system 10 is illustratedin the drawings and is described herein as merely one example of a widevariety of well systems in which the principles of this disclosure canbe utilized. It should be clearly understood that the principles of thisdisclosure are not limited at all to any of the details of the wellsystem 10, or components thereof, depicted in the drawings or describedherein.

For example, it is not necessary in keeping with the principles of thisdisclosure for the wellbore 12 to include a generally vertical wellboresection 14 or a generally horizontal wellbore section 18. It is notnecessary for fluids 30 to be only produced from the formation 20 since,in other examples, fluids could be injected into a formation, fluidscould be both injected into and produced from a formation, etc.

It is not necessary for one each of the well screen 24 and variable flowresistance system 25 to be positioned between each adjacent pair of thepackers 26. It is not necessary for a single variable flow resistancesystem 25 to be used in conjunction with a single well screen 24. Anynumber, arrangement and/or combination of these components may be used.

It is not necessary for any variable flow resistance system 25 to beused with a well screen 24. For example, in injection operations, theinjected fluid could be flowed through a variable flow resistance system25, without also flowing through a well screen 24.

It is not necessary for the well screens 24, variable flow resistancesystems 25, packers 26 or any other components of the tubular string 22to be positioned in uncased sections 14, 18 of the wellbore 12. Anysection of the wellbore 12 may be cased or uncased, and any portion ofthe tubular string 22 may be positioned in an uncased or cased sectionof the wellbore, in keeping with the principles of this disclosure.

It should be clearly understood, therefore, that this disclosuredescribes how to make and use certain examples, but the principles ofthe disclosure are not limited to any details of those examples.Instead, those principles can be applied to a variety of other examplesusing the knowledge obtained from this disclosure.

It will be appreciated by those skilled in the art that it would bebeneficial to be able to regulate flow of the fluids 30 into the tubularstring 22 from each zone of the formation 20, for example, to preventwater coning 32 or gas coning 34 in the formation. Other uses for flowregulation in a well include, but are not limited to, balancingproduction from (or injection into) multiple zones, minimizingproduction or injection of undesired fluids, maximizing production orinjection of desired fluids, etc.

Examples of the variable flow resistance systems 25 described more fullybelow can provide these benefits by increasing resistance to flow if afluid velocity increases beyond a selected level (e.g., to therebybalance flow among zones, prevent water or gas coning, etc.), and/orincreasing resistance to flow if a fluid viscosity decreases below aselected level (e.g., to thereby restrict flow of an undesired fluid,such as water or gas, in an oil producing well).

As used herein, the term “viscosity” is used to indicate any of therheological properties including kinematic viscosity, yield strength,viscoplasticity, surface tension, wettability, etc.

Whether a fluid is a desired or an undesired fluid depends on thepurpose of the production or injection operation being conducted. Forexample, if it is desired to produce oil from a well, but not to producewater or gas, then oil is a desired fluid and water and gas areundesired fluids. If it is desired to produce gas from a well, but notto produce water or oil, the gas is a desired fluid, and water and oilare undesired fluids. If it is desired to inject steam into a formation,but not to inject water, then steam is a desired fluid and water is anundesired fluid.

If gas is being flowed, it can be difficult to restrict flow of the gasusing conventional techniques, which typically involve interposing smalldiameter passages, orifices, etc. in the gas flow. Unfortunately, thesedevices can have an increased volumetric flow rate when gas is flowinginstead of oil or another fluid, and can result in erosion problems.

Note that, at downhole temperatures and pressures, hydrocarbon gas canactually be completely or partially in liquid phase. Thus, it should beunderstood that when the term “gas” is used herein, supercritical,liquid, condensate and/or gaseous phases are included within the scopeof that term.

Referring additionally now to FIG. 2, an enlarged scale cross-sectionalview of one of the variable flow resistance systems 25 and a portion ofone of the well screens 24 is representatively illustrated. In thisexample, a fluid composition 36 (which can include one or more fluids,such as oil and water, liquid water and steam, oil and gas, gas andwater, oil, water and gas, etc.) flows into the well screen 24, isthereby filtered, and then flows into an inlet 38 of the variable flowresistance system 25.

A fluid composition can include one or more undesired or desired fluids.Both steam and water can be combined in a fluid composition. As anotherexample, oil, water and/or gas can be combined in a fluid composition.

Flow of the fluid composition 36 through the variable flow resistancesystem 25 is resisted based on one or more characteristics (such asviscosity, velocity, density, etc.) of the fluid composition. The fluidcomposition 36 is then discharged from the variable flow resistancesystem 25 to an interior of the tubular string 22 via an outlet 40.

In other examples, the well screen 24 may not be used in conjunctionwith the variable flow resistance system 25 (e.g., in injectionoperations), the fluid composition 36 could flow in an oppositedirection through the various elements of the well system 10 (e.g., ininjection operations), a single variable flow resistance system could beused in conjunction with multiple well screens, multiple variable flowresistance systems could be used with one or more well screens, thefluid composition could be received from or discharged into regions of awell other than an annulus or a tubular string, the fluid compositioncould flow through the variable flow resistance system prior to flowingthrough the well screen, any other components could be interconnectedupstream or downstream of the well screen and/or variable flowresistance system, etc. Thus, it will be appreciated that the principlesof this disclosure are not limited at all to the details of the exampledepicted in FIG. 2 and described herein.

Although the well screen 24 depicted in FIG. 2 is of the type known tothose skilled in the art as a wire-wrapped well screen, any other typesor combinations of well screens (such as sintered, expanded, pre-packed,wire mesh, etc.) may be used in other examples. Additional components(such as shrouds, shunt tubes, lines, instrumentation, sensors, inflowcontrol devices, etc.) may also be used, if desired.

The variable flow resistance system 25 is depicted in simplified form inFIG. 2, but in a preferred example the system can include variouspassages and devices for performing various functions, as described morefully below. In addition, the system 25 can at least partially extendcircumferentially about the tubular string 22, or the system may beformed in a wall of a tubular structure interconnected as part of thetubular string.

In other examples, the system 25 may not extend circumferentially abouta tubular string or be formed in a wall of a tubular structure. Forexample, the system 25 could be formed in a flat structure, etc. Thesystem 25 could be in a separate housing that is attached to the tubularstring 22, or it could be oriented so that the axis of the outlet 40 isparallel to the axis of the tubular string. The system 25 could be on alogging string or attached to a device that is not tubular in shape. Anyorientation or configuration of the system 25 may be used in keepingwith the principles of this disclosure.

Referring additionally now to FIGS. 3A & B, a more detailedcross-sectional view of one example of the system 25 is representativelyillustrated. The system 25 is depicted in FIGS. 3A & B as if it is“unrolled” from its circumferentially extending configuration to agenerally planar configuration.

As described above, the fluid composition 36 enters the system 25 viathe inlet 38, and exits the system via the outlet 40. A resistance toflow of the fluid composition 36 through the system 25 varies based onone or more characteristics of the fluid composition.

The inlet 38, the outlet 40, and a flow passage 42 and flow chamber 44through which the fluid composition 36 flows between the inlet and theoutlet, are elements of a vortex device 46 which restricts flow of thefluid composition based on certain characteristics of the fluidcomposition. Rotational flow of the fluid composition 36 increases inthe chamber 44, thereby increasing restriction to flow through thechamber, for example, when a velocity of the fluid compositionincreases, when a viscosity of the fluid composition decreases, when adensity of the fluid composition increases, and/or when a ratio ofdesired fluid to undesired fluid in the fluid composition decreases.

As depicted in FIG. 3A, the chamber 44 is generally cylindrical-shaped,and the flow passage 42 intersects the chamber tangentially, so thatfluid entering the chamber via the inlet 48 tends to flow clockwise (asviewed in FIG. 3A) about the outlet 40. A bypass passage 50 intersectsthe passage 42 downstream of the inlet 38, and the bypass passage alsointersects the chamber 44 tangentially. However, fluid entering thechamber 44 through the bypass passage 50 via an inlet 52 tends to flowcounterclockwise (as viewed in FIG. 3A) about the outlet 40.

In FIG. 3A, a relatively high velocity and/or low viscosity fluidcomposition 36 flows through the flow passage 42 from the system inlet38 to the flow chamber 44. In contrast, a relatively low velocity and/orhigh viscosity fluid composition 36 flows through the flow passage 42 tothe chamber 44 in FIG. 3B.

Only a small proportion of the fluid composition 36 flows to the chamber44 via the bypass passage 50 in FIG. 3A. Thus, a substantial proportionof the fluid composition 36 rotates in the chamber 44, spiraling withincreasing rotational velocity toward the outlet 40. Note that therotation of the fluid composition 36 at the outlet 40 will increase asthe velocity of the fluid composition entering the inlet 38 increases,and as a viscosity of the fluid composition decreases.

A substantially larger proportion of the fluid composition flows to thechamber 44 via the bypass passage 50 in FIG. 3B. In this example, theflows entering the chamber 44 via the inlets 48, 52 are about equal.These flows effectively “cancel” or counteract each other, so that thereis relatively little rotational flow of the fluid composition 36 in thechamber 44.

It will be appreciated that the much more circuitous flow path taken bythe fluid composition 36 in the example of FIG. 3A dissipates more ofthe fluid composition's energy at the same flow rate and, thus, resultsin more resistance to flow, as compared to the much more direct flowpath taken by the fluid composition in the example of FIG. 3B. If oil isa desired fluid, and water and/or gas are undesired fluids, then it willbe appreciated that the variable flow resistance system 25 of FIGS. 3A &B will provide less resistance to flow of the fluid composition 36 whenit has an increased ratio of desired to undesired fluid therein, andwill provide greater resistance to flow when the fluid composition has adecreased ratio of desired to undesired fluid therein.

Since the chamber 44 in this example has a cylindrical shape with acentral outlet 40, and the fluid composition 36 (at least in FIG. 3A)spirals about the chamber, increasing in velocity as it nears theoutlet, driven by a pressure differential from the inlet 44 to theoutlet, the chamber may be referred to as a “vortex” chamber.

Circular flow inducing structures 54 are used in the chamber 44 in theconfiguration of FIGS. 3A & B. The structures 54 operate to maintaincircular flow of the fluid composition 36 about the outlet 40, or atleast to impede inward flow of the fluid composition toward the outlet,when the fluid composition does flow circularly about the outlet.Openings 56 in the structures 54 permit the fluid composition 36 toeventually flow inward to the outlet 40.

As discussed above, in FIG. 3A, the vortex device 46 is depicted in asituation in which an increased velocity and/or reduced viscosity of thefluid composition 36 results in a substantial proportion of the fluidcomposition flowing into the chamber 44 via the inlet 48. The fluidcomposition 36, thus, spirals about the outlet 40 in the chamber 44, anda resistance to flow through the vortex device 46 increases. A reducedviscosity can be due to a relatively low ratio of desired fluid toundesired fluid in the fluid composition 36.

Relatively little of the fluid composition 36 flows into the chamber 44via the inlet 52 in FIG. 3A, because the flow passage 50 is branchedfrom the flow passage 42 in a manner such that most of the fluidcomposition remains in the flow passage 42. At relatively highvelocities, high densities and/or low viscosities, the fluid composition36 tends to flow past the flow passage 50.

In FIG. 3B, a velocity of the fluid composition 36 has decreased and/ora viscosity of the fluid composition has increased, and as a result,proportionately more of the fluid composition flows from the passage 42and via the passage 50 to the inlet 52. The increased viscosity of thefluid composition 36 may be due to an increased ratio of desired toundesired fluids in the fluid composition.

Since, in FIG. 3B, the flows into the chamber 44 from the two inlets 48,52 are oppositely directed (or at least the flow of the fluidcomposition through the inlet 52 opposes the flow through the inlet 48),they counteract each other. Thus, the fluid composition 36 flows moredirectly to the outlet 40 and a resistance to flow through the vortexdevice 46 is decreased, and the fluid composition has reduced (or no)rotation at the outlet 40.

Referring additionally now to FIG. 4, another configuration of thevariable flow resistance system 25 is representatively illustrated. Inthis configuration, the vortex device 46 is used in series with twoadditional vortex devices 58, 60. Although three vortex devices 46, 58,60 are depicted in FIG. 4, it will be appreciated that any number ofvortex devices may be connected in series, in keeping with theprinciples of this disclosure.

An outlet 62 of the vortex device 46 corresponds to an inlet of thevortex device 58, and an outlet 64 of the vortex device 58 correspondsto an inlet of the vortex device 60. The fluid composition 36 flows fromthe system 25 inlet 38 to the chamber 44, from the chamber 44 to thevortex device 58 via the outlet/inlet 62, from the outlet/inlet 62 to avortex chamber 66 of the vortex device 58, from the chamber 66 to thevortex device 60 via the outlet/inlet 64, from the outlet/inlet 64 to avortex chamber 68 of the vortex device 60, and from the chamber 68 tothe outlet 40 of the system 25.

Each of the vortex devices 58, 60 includes two passages 70, 72 and 74,76, respectively, which function somewhat similar to the passages 42, 50of the vortex device 46. However, the proportions of the fluidcomposition 36 which flows through each of the passages 70, 72 and 74,76 varies based on a rotation of the fluid composition as it enters therespective vortex device 58, 60, as described more fully below.

Referring additionally now to FIG. 5, a cross-sectional view of thevariable flow resistance system 25 is representatively illustrated, asviewed along line 5-5 of FIG. 4. In this view, the manner in which theoutlet/inlet 62 and outlet/inlet 64 provide fluid communication betweenthe vortex devices 46, 58, 60 can be readily seen.

In FIG. 5, it may also be seen that the vortex devices 46, 58, 60 are“stacked” in a compact manner, alternating orientation back and forth.However, it will be appreciated that the vortex devices 46, 58, 60 couldbe otherwise arranged, in keeping with the principles of thisdisclosure.

Referring additionally now to FIGS. 6A & B, the variable flow resistancesystem 25 of FIGS. 4 & 5 is depicted, with a relatively low viscosity,high density and/or high velocity fluid composition 36 flowing throughthe system in FIG. 6A, and with a relatively high viscosity, low densityand/or low velocity fluid composition flowing through the system in FIG.6B. These examples demonstrate how the resistance to flow through thesystem 25 varies based on certain characteristics of the fluidcomposition 36.

In FIG. 6A, significant spiraling flow of the fluid composition 36 ispresent in the vortex device 46 (similar to that described above inrelation to FIG. 3A). As a result, the fluid composition 36 is rotatingsignificantly when it flows from the chamber 44 to the vortex device 58via the outlet/inlet 62.

This rotational flow of the fluid composition 36 causes a greaterproportion of the fluid composition to flow through the passage 70, ascompared to the proportion of the fluid composition which flows throughthe passage 72. The manner in which the rotating fluid composition 36impinges on the curved walls of the passages 70, 72 at theirintersection with the outlet/inlet 62 causes this difference in theproportions of the fluid composition which flows through each of thepassages.

Since a greater proportion of the fluid composition 36 flows into thechamber 66 of the vortex device 58 via the passage 70, the fluidcomposition rotates within the chamber 66, similar to the manner inwhich the fluid composition flows spirally through the chamber 44 of thevortex device 46. This spiraling flow of the fluid composition 36through the chamber 66 generates resistance to flow, with the resistanceto flow increasing with increased rotational flow of the fluidcomposition in the chamber.

The fluid composition 36 rotates as it exits the chamber 66 via theoutlet/inlet 64. This rotational flow of the fluid composition 36 causesa greater proportion of the fluid composition to flow through thepassage 74, as compared to the proportion of the fluid composition whichflows through the passage 76. Similar to that described above for thevortex chamber 58, the manner in which the rotating fluid composition 36impinges on the curved walls of the passages 74, 76 at theirintersection with the outlet/inlet 64 causes this difference in theproportions of the fluid composition which flows through each of thepassages.

Since a greater proportion of the fluid composition 36 flows into thechamber 68 of the vortex device 60 via the passage 74, the fluidcomposition rotates within the chamber 68, similar to the manner inwhich the fluid composition flows spirally through the chamber 66 of thevortex device 58. This spiraling flow of the fluid composition 36through the chamber 68 generates resistance to flow, with the resistanceto flow increasing with increased rotational flow of the fluidcomposition in the chamber.

Thus, with the relatively high velocity and/or low viscosity fluidcomposition 36 in FIG. 6A, rotational flow and resistance to flow isincreased in each of the vortex devices 46, 58, 60, so that overall flowresistance is much greater than that which would have been provided byonly the single vortex device 46. In addition, the rotational flowthrough the chambers 66, 68 of the vortex devices 58, 60 is due to therotational flow of the fluid composition 36 at each of the outlet/inlets62, 64.

In FIG. 6B, a relatively high viscosity and/or low velocity fluidcomposition 36 flows through the system 25. Note that rotational flow ofthe fluid composition 36 in each of the chambers 44, 66, 68 issignificantly reduced, and so the resistance to flow of the fluidcomposition through the chambers is also significantly reduced. Thus,the resistance to flow of the relatively high viscosity and/or lowvelocity fluid composition 36 is much less in FIG. 6B, as compared tothe resistance to flow of the relatively low viscosity and/or highvelocity fluid composition in FIG. 6A.

Note that any of the features of any of the configurations of the system25 described above may be included in any of the other configurations ofthe system and, thus, it should be understood that these features arenot exclusive to any one particular configuration of the system. Thesystem 25 can be used in any type of well system (e.g., not only in thewell system 10), and for accomplishing various purposes in various welloperations, including but not limited to injection, stimulation,completion, production, conformance, drilling operations, etc.

It will be appreciated that the system 25 of FIGS. 4-6B providessignificant advancements to the art of controlling flow in a well. Theresistance to flow of the fluid composition 36 through the system 25 canbe substantially increased by connecting the vortex devices 46, 58, 60in series, and by resisting flow of the fluid composition in response toits rotation as it passes from one vortex device to the next.

The above disclosure provides to the art a variable flow resistancesystem 25 for use in a subterranean well. The system 25 can include avortex device 58 or 60 through which a fluid composition 36 flows. Aresistance to flow of the fluid composition 36 through the vortex device58 or 60 is dependent on a rotation of the fluid composition 36 at aninlet 62 or 64 to the vortex device 58 or 60.

The resistance to flow of the fluid composition 36 through the vortexdevice 58 or 60 can increase in response to an increased rotation of thefluid composition 36 at the inlet 62 or 64 to the vortex device 58 or60.

The rotation of the fluid composition 36 at the inlet 62 or 64 canincrease in response to a decrease in viscosity of the fluid composition36.

The rotation of the fluid composition 36 at the inlet 62 or 64 canincrease in response to an increase in velocity of the fluid composition36.

The rotation of the fluid composition 36 at the inlet 62 or 64 canincrease in response to a decrease in a ratio of desired to undesiredfluid in the fluid composition 36.

An outlet 64 of the vortex device 58 can comprise an inlet 64 of anothervortex device 60. The inlet 64 of the vortex device 60 can comprise anoutlet 64 of another vortex device 58.

The vortex device 58 can comprise at least first and second passages 70,72 which receive the fluid composition 36 from an outlet 62 of anothervortex device 46. A difference in proportions of the fluid composition36 which flows through the respective first and second passages 70, 72is dependent on the rotation of the fluid composition 36 at the outlet62. The difference in the proportions of the fluid composition 36 whichflows through the first and second passages 70, 72 may increase inresponse to an increase in velocity of the fluid composition 36.

Rotation of the fluid composition 36 in a vortex chamber 66 increases inresponse to an increase in the difference in the proportions of thefluid composition 36 which flows through the first and second passages70, 72.

The above disclosure also describes a variable flow resistance system 25which can include a first vortex 46 device having an outlet 62, and asecond vortex device 58 which receives a fluid composition 36 from theoutlet 62 of the first vortex device 46. A resistance to flow of thefluid composition 36 through the second vortex device 58 can bedependent on a rotation of the fluid composition 36 at the outlet 62 ofthe first vortex device 46.

The rotation of the fluid composition 36 at the outlet 62 may increasein response to a decrease in viscosity of the fluid composition 36, inresponse to an increase in velocity of the fluid composition 36 and/orin response to a decrease in a ratio of desired to undesired fluid inthe fluid composition 36.

The resistance to flow of the fluid composition 36 through the secondvortex device 58 can increase in response to an increase in the rotationof the fluid composition 36 at the outlet 62 of the first vortex device46.

An outlet 64 of the second vortex device 58 can comprise an inlet 64 ofa third vortex device 60.

The second vortex device 58 can include at least first and secondpassages 70, 72 which receive the fluid composition 36 from the outlet62 of the first vortex device 46. A difference in proportions of thefluid composition 36 which flow through the respective first and secondpassages 70, 72 is dependent on the rotation of the fluid composition 36at the outlet 62 of the first vortex device 46.

The difference in the proportions of the fluid composition 36 whichflows through the first and second passages 70, 72 may increase inresponse to an increase in velocity of the fluid composition 36.

Rotation of the fluid composition 36 in a vortex chamber 66 of thesecond vortex device 58 may increase in response to an increase in thedifference in the proportions of the fluid composition 36 which flowsthrough the first and second passages 70, 72.

The above disclosure also describes a variable flow resistance system 25which can include a first vortex device 46 which causes increasedrotation of a fluid composition 36 at an outlet 62 of the first vortexdevice 46 in response to an increase in a velocity of the fluidcomposition 36, and a second vortex device 58 which receives the fluidcomposition 36 from the outlet 62 of the first vortex device 46. Aresistance to flow of the fluid composition 36 through the second vortexdevice 58 may be dependent on the rotation of the fluid composition 36at the outlet 62 of the first vortex device 46.

Note that the vortex devices 46, 58, 60 may be of the type known tothose skilled in the art as fluid “diodes.”

A well device (e.g., the variable flow resistance system 25) forinstallation in a wellbore 12 in a subterranean zone (e.g., in formation20) can include a first fluid diode (e.g., vortex device 46) comprising:a first interior surface 80 (see FIGS. 4 & 5) that defines a firstinterior chamber 44, and an outlet 62 from the first interior chamber44, the first interior surface 80 operable to direct fluid (e.g., fluidcomposition 36) to rotate in a rotational direction through the outlet62; and a second fluid diode (e.g., vortex device 58) comprising: asecond interior surface 82 that defines a second interior chamber 66 influid communication with the outlet 62, the second interior surface 82operable to direct fluid (e.g., fluid composition 36) to rotate in therotational direction in response to receiving the fluid rotating in therotational direction through the outlet 62.

The second fluid diode can include an inlet (in the FIGS. 4-6B example,the inlet of the chamber 58 is the same as the outlet 62 of the chamber44) operable to receive the fluid 36 directly from the outlet 62. Thesecond interior chamber 66 can comprise: a cylindroidal chamber 66, afirst flow passage 70 from the inlet 62 to the cylindroidal chamber 66,and a second flow passage 72 from the inlet 62 to the cylindroidalchamber 66.

The second interior surface 82 may be operable to direct a majority ofthe fluid 36 to the first flow passage 70 in response to receiving thefluid 36 rotating in the rotational direction through the inlet 62.

The first interior surface 80 may be operable to direct fluid 36 torotate in a rotational direction about a first axis of rotation 84, andthe second interior surface 82 may be operable to direct fluid 36 torotate in a rotational direction about a second axis of rotation 86. Thefirst axis of rotation 84 can be parallel to the second axis of rotation86.

The first fluid diode 46 and the second fluid diode 58 may be in fluidcommunication between an interior and an exterior of the well device(e.g., the variable flow resistance system 25). The first fluid diode 46and the second fluid diode 58 can be in fluid communication between theinterior and the exterior to communicate production fluid 36 from theexterior of the well device 25 to the interior of the well device 25.The well device 25 may comprise a section of a completion string 22.

The first and second fluid diodes 46, 58 can be in fluid communicationbetween the interior and the exterior to communicate injection fluid 36from the interior of the well device 25 to the exterior of the welldevice 25. The well device 25 may comprise a section of a working string22.

The outlet 62 can comprise a first outlet 62, the first fluid diode 46can further comprise a first inlet 38, the first interior surface 80 mayinclude a first side perimeter surface 80 and first opposing endsurfaces 88, a greatest distance between the first opposing end surfaces88 can be smaller than a largest dimension of the first opposing endsurfaces 88, and the first side perimeter surface 80 may be operable todirect flow from the first inlet 38 to rotate about the first outlet 62.

The second fluid diode 58 can comprise a second inlet 62 operable toreceive the fluid 36 directly from the first outlet 62, the secondinterior surface 82 may include a second side perimeter surface 82 andsecond opposing end surfaces 90, a greatest distance between the secondopposing end surfaces 90 may be smaller than a largest dimension of thesecond opposing end surfaces 90, and the second side perimeter surface82 can be operable to direct flow from the second inlet 62 to rotateabout a second outlet 64.

A method of controlling flow in a wellbore 12 in a subterranean zone 20can include communicating fluid 36 through a first fluid diode 46 and asecond fluid diode 58 in a flow path between an interior and an exteriorof a well device 25 in the subterranean zone 20. Communicating the fluid36 through the first fluid diode 46 and the second fluid diode 58 cancause the fluid 36 to rotate within the first fluid diode 46 in arotational direction and to rotate within the second fluid diode 58 inthe rotational direction.

The fluid 36 may comprise a production or injection fluid.

Communicating the fluid 36 through the first fluid diode 46 and thesecond fluid diode 58 can control a resistance to a flow of the fluid 36between the interior and the exterior based on a characteristic of theflow. The characteristic may comprise at least one of viscosity,velocity or density.

A resistance to flow through the second fluid diode 58 can be based atleast in part on a characteristic of inflow received by the second fluiddiode 58 from the first fluid diode 46.

It is to be understood that the various examples described above may beutilized in various orientations, such as inclined, inverted,horizontal, vertical, etc., and in various configurations, withoutdeparting from the principles of the present disclosure. The embodimentsillustrated in the drawings are depicted and described merely asexamples of useful applications of the principles of the disclosure,which are not limited to any specific details of these embodiments.

Of course, a person skilled in the art would, upon a carefulconsideration of the above description of representative embodiments,readily appreciate that many modifications, additions, substitutions,deletions, and other changes may be made to these specific embodiments,and such changes are within the scope of the principles of the presentdisclosure. Accordingly, the foregoing detailed description is to beclearly understood as being given by way of illustration and exampleonly, the spirit and scope of the present invention being limited solelyby the appended claims and their equivalents.

What is claimed is:
 1. A well device for installation in a wellbore in asubterranean zone, comprising: a first fluid diode comprising: a firstinterior surface that defines a first interior chamber, and an outletfrom the first interior chamber, the first interior surface operable todirect fluid to rotate in a rotational direction through the outlet; anda second fluid diode comprising: an inlet operable to receive the fluiddirectly from the outlet, and a second interior surface that defines asecond interior chamber in fluid communication with the outlet, whereinthe second interior chamber comprises a cylindroidal chamber, a firstflow passage from the inlet to the cylindroidal chamber, and a secondflow passage from the inlet to the cylindroidal chamber, and wherein thesecond interior surface is operable to direct fluid to rotate in therotational direction in response to receiving the fluid rotating in therotational direction through the outlet.
 2. The well device of claim 1,wherein the second interior surface is operable to direct a majority ofthe fluid to the first flow passage in response to receiving the fluidrotating in the rotational direction through the inlet.
 3. The welldevice of claim 1, wherein the first interior surface is operable todirect fluid to rotate in the rotational direction about a first axis ofrotation, and the second interior surface is operable to direct fluid torotate in the rotational direction about a second axis of rotation. 4.The well device of claim 3, wherein the first axis of rotation isparallel to the second axis of rotation.
 5. The well device of claim 1,wherein the first fluid diode and the second fluid diode are in fluidcommunication between an interior and an exterior of the well device. 6.The well device of claim 5, wherein the first fluid diode and the secondfluid diode are in fluid communication between the interior and theexterior to communicate production fluid from the exterior of the welldevice to the interior of the well device.
 7. The well device of claim6, wherein the well device comprises a section of a completion string.8. The well device of claim 5, wherein the first and second fluid diodesare in fluid communication between the interior and the exterior tocommunicate injection fluid from the interior of the well device to theexterior of the well device.
 9. The well device of claim 8, wherein thewell device comprises a section of a working string.
 10. The well deviceof claim 1, wherein the outlet comprises a first outlet, the first fluiddiode further comprises a first inlet, the first interior surfaceincludes a first side perimeter surface and first opposing end surfaces,a greatest distance between the first opposing end surfaces is smallerthan a largest dimension of the first opposing end surfaces, and thefirst side perimeter surface is operable to direct flow from the firstinlet to rotate about the first outlet.
 11. The well device of claim 10,wherein the second fluid diode further comprises a second inlet operableto receive the fluid directly from the first outlet, the second interiorsurface includes a second side perimeter surface and second opposing endsurfaces, a greatest distance between the second opposing end surfacesis smaller than a largest dimension of the second opposing end surfaces,and the second side perimeter surface is operable to direct flow fromthe second inlet to rotate about a second outlet.
 12. A method ofcontrolling flow in a wellbore in a subterranean zone, comprising:providing first and second fluid diodes, each fluid diode comprising aninlet which branches into a pair of flow passages which selectivelydeliver fluid to a vortex chamber having an outlet, wherein the inlet ofthe second fluid diode receives the fluid from the outlet of the firstfluid diode; and communicating the fluid through the first fluid diodeand the second fluid diode in a flow path between an interior and anexterior of a well device in the subterranean zone, wherein thecommunicating causes the fluid to rotate within the first fluid diode ina rotational direction and to rotate within the second fluid diode inthe rotational direction.
 13. The method of claim 12, wherein the fluidcomprises a production fluid.
 14. The method of claim 12, wherein thefluid comprises an injection fluid.
 15. The method of claim 12, whereinthe communicating controls a resistance to a flow of the fluid betweenthe interior and the exterior based on a characteristic of the flow. 16.The method of claim 15, wherein the characteristic comprises at leastone of viscosity, velocity and density.
 17. The method of claim 15,wherein a resistance to flow through the second fluid diode is based atleast in part on a characteristic of inflow received by the second fluiddiode from the first fluid diode.